This research introduces JuMBRo (Jumping Mobile Balancing Robot), a two-wheeled self-balancing robot (TWSBR) capable of jumping while balancing using Model Predictive Control (MPC). JuMBRo’s jumping ability significantly enhances its mobility, allowing it to access areas that would otherwise be inaccessible to non-jumping wheeled robots. With only four actuators, JuMBRo presents a viable alternative to legged mobile robots. The robot features a five-bar linkage mechanism that enables vertical movement and pitch angle adjustment, facilitating both jumping and body angle control during maneuvering.  Forward and inverse kinematics equations are derived and applied to control the body angle. The body angle is controlled by adjusting the leg extension through coordinated actuation of the five-bar linkage, enabling manipulation of the pitch orientation of the body during balancing. The MPC controller, based on a linearized discrete-time state-space model obtained via the Euler-Lagrange method, maintains balance, while a cascade Proportional-Integral-Derivative (PID) controller ensures stable station-keeping, helping the robot maintain its position. Experimental results demonstrate JuMBRo’s ability to overcome obstacles, maintain position, and recover balance when subjected to disturbances such as horizontal pushes. These findings underscore the effectiveness of the proposed approach and JuMBRo’s potential as a viable alternative to legged robots in various applications.